Solve 1/a^2-4/frac{4a^2{9}}=1

$$\frac { 1 } { a ^ { 2 } } - \frac { 4 } { \frac { 4 a ^ { 2 } } { 9 } } = 1$$

Solve for a

$$a=-2\sqrt{2}i\approx -0-2.828427125i$$

$$a=2\sqrt{2}i\approx 2.828427125i$$

Steps by Finding Square Root

Variable a cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by a^{2}.

$$1-\frac{9}{4}\times 4=a^{2}$$

Multiply -\frac{9}{4} and 4 to get -9.

$$1-9=a^{2}$$

Subtract 9 from 1 to get -8.

$$-8=a^{2}$$

Swap sides so that all variable terms are on the left hand side.

$$a^{2}=-8$$

The equation is now solved.

$$a=2\sqrt{2}i a=-2\sqrt{2}i$$

Steps Using the Quadratic Formula

Variable a cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by a^{2}.

$$1-\frac{9}{4}\times 4=a^{2}$$

Multiply -\frac{9}{4} and 4 to get -9.

$$1-9=a^{2}$$

Subtract 9 from 1 to get -8.

$$-8=a^{2}$$

Swap sides so that all variable terms are on the left hand side.

$$a^{2}=-8$$

Add 8 to both sides.

$$a^{2}+8=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and 8 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$a=\frac{0±\sqrt{0^{2}-4\times 8}}{2}$$

Square 0.

$$a=\frac{0±\sqrt{-4\times 8}}{2}$$

Multiply -4 times 8.

$$a=\frac{0±\sqrt{-32}}{2}$$

Take the square root of -32.

$$a=\frac{0±4\sqrt{2}i}{2}$$

Now solve the equation a=\frac{0±4\sqrt{2}i}{2} when ± is plus.

$$a=2\sqrt{2}i$$

Now solve the equation a=\frac{0±4\sqrt{2}i}{2} when ± is minus.

$$a=-2\sqrt{2}i$$

The equation is now solved.

$$a=2\sqrt{2}i a=-2\sqrt{2}i$$